scholarly journals A Note on Conditioning and Stochastic Domination for Order Statistics

2008 ◽  
Vol 45 (2) ◽  
pp. 575-579 ◽  
Author(s):  
Devdatt Dubhashi ◽  
Olle Häggström
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Conditional Distribution ◽  
Random Variables ◽  
Stochastic Domination

For an order statistic (X1:n,…,Xn:n) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (Xi+1:n,…,Xn:n) given Xi:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

scholarly journals A Note on Conditioning and Stochastic Domination for Order Statistics

2008 ◽  
Vol 45 (02) ◽  
pp. 575-579
Author(s):  
Devdatt Dubhashi ◽  
Olle Häggström
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Conditional Distribution ◽  
Random Variables ◽  
Stochastic Domination

For an order statistic (X 1:n ,…,X n:n ) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (X i+1:n ,…,X n:n ) given X i:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

scholarly journals Complete convergence for arrays of ratios of order statistics

2019 ◽  
Vol 17 (1) ◽  
pp. 439-451
Author(s):  
Yu Miao ◽  
Huanhuan Ma ◽  
Shoufang Xu ◽  
Andre Adler
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Complete Convergence ◽  
Pareto Distribution ◽  
Random Variables ◽  
Independent Random Variables

Abstract Let {Xn,k, 1 ≤ k ≤ mn, n ≥ 1} be an array of independent random variables from the Pareto distribution. Let Xn(k) be the kth largest order statistic from the nth row of the array and set Rn,in,jn = Xn(jn)/Xn(in) where jn < in. The aim of this paper is to study the complete convergence of the ratios {Rn,in,jn, n ≥ 1}.

Two characterizations of the geometric distribution

1980 ◽  
Vol 17 (02) ◽  
pp. 570-573 ◽  
Author(s):  
Barry C. Arnold
Keyword(s):  
Positive Integer ◽  
Order Statistics ◽  
Conditional Distribution ◽  
Geometric Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Mild Conditions ◽  
Independent Identically Distributed

Let X 1, X 2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X 1:n , X 2:n , …, Xn :n. If the Xi 's have a geometric distribution then the conditional distribution of Xk +1:n – Xk :n given Xk+ 1:n – Xk :n &gt; 0 is the same as the distribution of X 1:n–k . Also the random variable X 2:n – X 1:n is independent of the event [X 1:n = 1]. Under mild conditions each of these two properties characterizes the geometric distribution.

Distribution of minimum path

1975 ◽  
Vol 12 (01) ◽  
pp. 164-166
Author(s):  
Aaron Tenenbein
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
The Other ◽  
Minimum Path

Let Y, X 1, X 2, …, Xn be a set of n + 1 independently and uniformly distributed random variables on the interval (0, 1). The distribution of the length of the minimum path starting at Y which covers the other n points is derived. The solution is interesting in that it involves finding the distribution of an order statistic of a function of order statistics.

Characterizations via conditional distributions

1977 ◽  
Vol 14 (04) ◽  
pp. 806-816
Author(s):  
Robert H. Berk
Keyword(s):  
Order Statistics ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Exponential Family ◽  
Random Variables ◽  
Independent Random Variables ◽  
Conditional Distributions

For independent random variablesXandY,if the conditional distribution ofXgivenX+Ysatisfies certain conditions, then the joint distribution ofXandYis a member of a certain one-parameter exponential family. Extensions fornindependent random variables are given. A characterization for independent random variables involving order statistics is also given.

Distribution of minimum path

1975 ◽  
Vol 12 (1) ◽  
pp. 164-166
Author(s):  
Aaron Tenenbein
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
The Other ◽  
Minimum Path

Let Y, X1, X2, …, Xn be a set of n + 1 independently and uniformly distributed random variables on the interval (0, 1). The distribution of the length of the minimum path starting at Y which covers the other n points is derived. The solution is interesting in that it involves finding the distribution of an order statistic of a function of order statistics.

scholarly journals On order statistics from nonidentical discrete random variables

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 192-196
Author(s):  
Bahadır Yüzbaşı ◽  
Yunus Bulut ◽  
Mehmet Güngör
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
Integral Form ◽  
Discrete Case ◽  
Discrete Random Variables

AbstractIn this study, pf and df of single order statistic of nonidentical discrete random variables are obtained. These functions are also expressed in integral form. Finally, pf and df of extreme of order statistics of random variables for the nonidentical discrete case are given.

scholarly journals ON STOCHASTIC COMPARISONS OF ORDER STATISTICS FROM HETEROGENEOUS EXPONENTIAL SAMPLES

2019 ◽  
pp. 1-6
Author(s):  
Yaming Yu
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Open Problem ◽  
Hazard Rate ◽  
Random Variables ◽  
Stochastic Comparisons ◽  
Heterogeneous Sample ◽  
Exponential Random Variables ◽  
Hazard Rate Ordering

Abstract We show that the kth order statistic from a heterogeneous sample of n ≥ k exponential random variables is larger than that from a homogeneous exponential sample in the sense of star ordering, as conjectured by Xu and Balakrishnan [14]. As a consequence, we establish hazard rate ordering for order statistics between heterogeneous and homogeneous exponential samples, resolving an open problem of Pǎltǎnea [11]. Extensions to general spacings are also presented.

scholarly journals OPTIMAL MOMENT INEQUALITIES FOR ORDER STATISTICS FROM NONNEGATIVE RANDOM VARIABLES

2019 ◽  
pp. 1-15
Author(s):  
Nickos Papadatos
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Random Variables ◽  
Upper Bounds ◽  
Moment Inequalities ◽  
Population Mean ◽  
Sample Minimum ◽  
Independent Identically Distributed

We obtain the best possible upper bounds for the moments of a single-order statistic from independent, nonnegative random variables, in terms of the population mean. The main result covers the independent identically distributed case. Furthermore, the case of the sample minimum for merely independent (not necessarily identically distributed) random variables is treated in detail.

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